Question

day 4 - thursday, september 11th fill in the missing statements in the proof: statements reasons 1. ∠x and ∠y are complements of ∠z. 1. given 2. m∠x + m∠z = 90° 2. definition of complements 3. m∠y + m∠z = 90° 3. definition of complements 4. m∠x = m∠y 4. 5. ∠x ≅ ∠y 5. definition of congruent angles

Explanation:

Step1: Start from equations

We have $m\angle X + m\angle Z=90^{\circ}$ and $m\angle Y + m\angle Z = 90^{\circ}$.

Step2: Solve for $m\angle X$ and $m\angle Y$

From $m\angle X + m\angle Z=90^{\circ}$, we get $m\angle X=90^{\circ}-m\angle Z$. From $m\angle Y + m\angle Z = 90^{\circ}$, we get $m\angle Y=90^{\circ}-m\angle Z$.

Step3: Use substitution property

Since $m\angle X=90^{\circ}-m\angle Z$ and $m\angle Y=90^{\circ}-m\angle Z$, by substitution, $m\angle X = m\angle Y$. So the reason for statement 4 is the substitution property of equality.

Answer:

1. Substitution property of equality